On the Use of Monotonicity-Preserving Interpolatory Techniques in Multilevel Schemes for Balance Laws

doi:10.1007/s42967-023-00332-3

Communications on Applied Mathematics and Computation ›› 2024, Vol. 6 ›› Issue (2): 1319-1341.doi: 10.1007/s42967-023-00332-3

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On the Use of Monotonicity-Preserving Interpolatory Techniques in Multilevel Schemes for Balance Laws

Antonio Baeza¹, Rosa Donat¹, Anna Martínez-Gavara²

1. Department de Matemàtiques, Universitat de València, Dr. Moliner, 50, 46100 Burjassot, Valencia, Spain;
2. Department d'Estadistica i Investigació Operativa, Universitat de València, Dr. Moliner, 50, 46100 Burjassot, Valencia, Spain

Received:2023-01-18 Revised:2023-09-28 Accepted:2023-09-29 Online:2024-01-11 Published:2024-01-11
Contact: Antonio Baeza,E-mail:bamanan@uv.es;Rosa Donat,E-mail:donat@uv.es;Anna Martínez-Gavara,E-mail:gavara@uv.es E-mail:bamanan@uv.es;donat@uv.es;gavara@uv.es
Supported by:
Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. A. Baeza and R. Donat have been supported by Grant PID2020-117211GB-I00 funded by MCIN/AEI/10.13039/501100011033 and by Grant CIAICO/2021/227 funded by the Generalitat Valenciana. A. Martínez-Gavara has been supported by the Ministerio de Ciencia e Innovación of Spain (Grant Ref. PID2021-125709OB-C21) funded by MCIN/AEI/10.13039/501100011033/FEDER, UE and by the Generalitat Valenciana (CIAICO/2021/224).

Abstract

Abstract: Cost-effective multilevel techniques for homogeneous hyperbolic conservation laws are very successful in reducing the computational cost associated to high resolution shock capturing numerical schemes. Because they do not involve any special data structure, and do not induce savings in memory requirements, they are easily implemented on existing codes and are recommended for 1D and 2D simulations when intensive testing is required. The multilevel technique can also be applied to balance laws, but in this case, numerical errors may be induced by the technique. We present a series of numerical tests that point out that the use of monotonicity-preserving interpolatory techniques eliminates the numerical errors observed when using the usual 4-point centered Lagrange interpolation, and leads to a more robust multilevel code for balance laws, while maintaining the efficiency rates observed for hyperbolic conservation laws.

Key words: Hyperbolic balance laws, Well-balanced schemes, Multilevel schemes, Harten’s multiresolution

Antonio Baeza, Rosa Donat, Anna Martínez-Gavara. On the Use of Monotonicity-Preserving Interpolatory Techniques in Multilevel Schemes for Balance Laws[J]. Communications on Applied Mathematics and Computation, 2024, 6(2): 1319-1341.

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References

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On the Use of Monotonicity-Preserving Interpolatory Techniques in Multilevel Schemes for Balance Laws

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